A fourth shop on Station Road: Lena and Marco have found a site for a fourth shop on Station Road. Fitting it out, with ovens, counters and a sign over the door, will cost $120,000.
Marco has forecast what the shop will bring in each year once its wages, rent and flour are paid: $30,000 in the first year, rising by $2,000 a year as more customers find it.
| Year | Net cash flow from the Station Road shop |
|---|---|
| 1 | $30,000 |
| 2 | $32,000 |
| 3 | $34,000 |
| 4 | $36,000 |
| 5 | $38,000 |
| Total, five years | $170,000 |
Each year's figure is a net cash flow: the money the shop brings in, minus the money it pays out, in that year. Added together over the five years they make the shop's total returns, $170,000.
The $120,000 spent on fitting it out is the capital cost. Take it off the total returns and the shop leaves $50,000 more than it cost. That $50,000 is the profit the investment makes over its life.
Is $50,000 a lot?: On its own, a dollar figure cannot say. $50,000 over five years would be a fine return on a $20,000 van and a poor one on a $2 million bakehouse.
To judge it, Lena needs the profit as a share of what she has to put in, the way a savings account quotes its interest as a percentage.
That share is the average rate of return (ARR): the profit an investment makes in an average year, as a percentage of its capital cost.
ARR = ((total returns − capital cost) ÷ years of use) ÷ capital cost × 100
The formula is on the formulae sheet you have in the exam. The years of use are the years the forecast covers: five for Station Road.
Capital cost
- What the investment costs to buy or set up, paid at the start
- Station Road: $120,000 to fit out the shop
Total returns
- Every year's net cash flow from the investment, added together
- Station Road: $170,000 over five years
Years of use
- How many years the returns are forecast for
- Station Road: 5 years
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Marco works out the ARR for Station Road in four short steps, and writes each one down. The order matters: take the capital cost off first, then find the average year, then compare it with the cost.
The Station Road shop, ARR
Add up the total returns
$30,000 + $32,000 + $34,000 + $36,000 + $38,000 = $170,000.
Take off the capital cost
$170,000 − $120,000 = $50,000.
This is what the shop earns over five years on top of paying back its cost.
Divide by the years of use
$50,000 ÷ 5 = $10,000 a year: the profit in an average year.
Divide by the capital cost, times 100
$10,000 ÷ $120,000 × 100 = 8.333..., so 8.33%.
Write the % sign. A rate of return is a percentage.
What 8.33% means: In an average year, the Station Road shop earns $8.33 for every $100 it cost, on top of paying back the $120,000.
The higher the ARR, the harder each dollar put into the investment is working.
| The slip | What it gives | Why it is wrong |
|---|---|---|
| Not taking off the capital cost | $170,000 ÷ 5 ÷ $120,000 × 100 = 28.33% | It counts the $120,000 the shop cost as if it were profit. |
| Not dividing by the years of use | $50,000 ÷ $120,000 × 100 = 41.67% | That is five years of profit, not one average year. |
| Dividing by the total returns | $10,000 ÷ $170,000 × 100 = 5.88% | The yearly profit is measured against what the shop cost, not what it brings in. |
| Stopping at the decimal | $10,000 ÷ $120,000 = 0.0833 | The rate is a percentage: times 100 and write the % sign. |
Round only at the end, to two decimal places. 8.3% or 8% is the same answer rounded further; 9% is not. Keep the units the case uses: if the figures are in $ millions, the answer is still just a percentage.
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What if the ovens are sold at the end?: Marco's forecast stops after five years. Suppose Lena and Marco then close the shop and sell its ovens and fittings for $10,000.
That $10,000 is money the investment brings back, so it belongs in the total returns. The price an asset can be sold for at the end of its use is its residual value (or scrap value).
Station Road with a $10,000 residual value
Total returns, residual value included
$170,000 + $10,000 = $180,000.
Take off the capital cost
$180,000 − $120,000 = $60,000.
Divide by the years of use
$60,000 ÷ 5 = $12,000 a year.
Divide by the capital cost, times 100
$12,000 ÷ $120,000 × 100 = 10.00%.
Add it to the returns, not to the cost: The residual value is a return, received in the last year. Add it to the total returns.
Taking it off the capital cost instead gives 10.91%, and leaving it out gives 8.33%. Once the case gives a price for selling the asset, both are wrong.
The returns do not always come as a neat table of yearly figures. Whatever shape they take, the first job is the same: find the total returns over the years of use. Then the four steps run exactly as before.
| How the case gives the returns | How to find the total returns |
|---|---|
| A figure for each year | Add every year's figure. |
| The same figure every year | Multiply it by the years of use. |
| Income and running costs for each year | Take each year's costs off its income, then add the years. |
| A yearly cost saving and extra revenue | Add the two for the yearly gain, then multiply by the years of use. |
| One total for the whole period | Use it as the total returns: nothing to add. |
| A price for selling the asset at the end | Add it to the other returns (the residual value). |
A table that starts at Year 0: Year 0 is the day the money is spent, so a table may show the capital cost there with a minus sign: Station Road's Year 0 would be −$120,000.
Adding every row, Year 0 included, gives $50,000 straight away: the cost is already taken off, so do not take it off again. And Year 0 is not a year of use: there are still five.
8.33%: is that enough?: Lena and Marco want any new project to earn at least 10% a year: their target, or criterion rate. On Marco's forecast, Station Road's ARR is 8.33%, so on this figure alone it falls short. With $10,000 from selling the fittings at the end, it just reaches 10.00%.
An ARR means most when it is set against something: the business's own target, the interest the same money would earn in a bank, or the interest a loan to pay for it would cost. A project whose ARR is below the interest on the loan that pays for it would not even cover its borrowing.
The higher the ARR, the better, as long as the forecast behind it is right.
What ARR does well
- It uses every year's returns over the whole life of the investment, not just the first few
- It gives a percentage, easy to set against a target, an interest rate or another project
- It shows how profitable the investment is, not only how fast its cost comes back
- It is quick to work out and easy to explain to the owners
What ARR leaves out
- When the returns arrive: a big return in year 1 and the same return in year 5 count the same
- The time value of money: a dollar received in five years is worth less than a dollar today
- How long the business waits to get its capital cost back
- How sure the forecast is: the further ahead the returns, the less reliable they are
| Year | Marco's forecast | A forecast that saves it all for the end |
|---|---|---|
| 1 | $30,000 | $10,000 |
| 2 | $32,000 | $10,000 |
| 3 | $34,000 | $10,000 |
| 4 | $36,000 | $10,000 |
| 5 | $38,000 | $130,000 |
| Total returns | $170,000 | $170,000 |
| ARR | 8.33% | 8.33% |
The same ARR, not the same shop: Both forecasts give an ARR of 8.33%. In the second, though, the shop has brought in only $40,000 of its $120,000 after four years, and everything rides on year 5, the year the forecast is least sure of.
ARR averages the returns, so it cannot see the difference. On Marco's forecast the shop pays back its cost in 3 years and 8 months (the payback period, 3.8.1); on the second it is well into year 5.
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How this comes up: As a two-mark calculation from a case: calculate the average rate of return (ARR), show all your working. It often sits next to a payback period worked from the same figures.
The returns come as a yearly table, a flat amount a year, income and costs, or a saving plus extra revenue, sometimes with a price for selling the asset at the end. Part of the task is building the total returns from them.
The two-mark calculation
- Write the formula: ARR = ((total returns − capital cost) ÷ years of use) ÷ capital cost × 100.
- Find the total returns and write that line down, residual value included.
- Take off the capital cost, then divide by the years of use, to get the average yearly profit.
- Divide by the capital cost and times 100. Give the answer to two decimal places with a % sign.
Three ways to lose a mark: No working. Where the question says show all your working, a correct answer on its own gets one mark of two.
No % sign. 0.0917 is not an answer; 9.17% is. The capital cost left in. Forgetting to take it off gives an answer several times too big.
Calculate the average rate of return (ARR) for Harbourside Cafés' coffee roaster (show all your working).
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